Writing Linear Equations Flashcard Review

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What is the difference between a positive slope and a negative slope?

Back

A positive slope means the line rises from left to right, while a negative slope means the line falls from left to right.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.

Front

How can you determine if a point (x, y) lies on a line represented by a linear equation?

Back

To determine if a point (x, y) lies on the line, substitute x into the equation and see if the resulting y value matches the y-coordinate of the point.

Front

What is a table of values in relation to linear equations?

Back

A table of values lists pairs of x and y coordinates that satisfy a linear equation, showing how y changes as x changes.